Semigroup Forum

, Volume 90, Issue 2, pp 532–544 | Cite as

Partial transformation monoids preserving a uniform partition

  • Serena Cicalò
  • Vítor H. Fernandes
  • Csaba SchneiderEmail author


The objective of this paper is to study the monoid of all partial transformations of a finite set that preserve a uniform partition. In addition to proving that this monoid is a quotient of a wreath product with respect to a congruence relation, we show that it is generated by 5 generators, we compute its order and determine a presentation on a minimal generating set.


Transformation monoids Uniform partitions Ranks  Presentations Partial transformations Wreath products  



Cicalò gratefully acknowledges support of FCT and PIDDAC, within the Project PTDC/MAT/69514/2006 of CAUL, and support of the Regione Sardegna, within the Project Master & Back, PR-MAB-A2009-837. She also thanks the Department of Mathematics of the University of Trento for its hospitality from 2011. Fernandes gratefully acknowledges support of FCT and PIDDAC, within the Projects ISFL-1-143 and PTDC/MAT/69514/2006 of CAUL. Schneider was supported by the research funds PTDC/MAT/101993/2008 (FCT), 302660/2013-5 (CNPq, Produtividade em Pesquisa), 475399/2013-7 (CNPq, Universal), and by APQ-00452-13 (Fapemig, Universal).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Serena Cicalò
    • 1
  • Vítor H. Fernandes
    • 2
    • 3
  • Csaba Schneider
    • 4
    Email author
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di CagliariCagliariItaly
  2. 2.Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade Nova de Lisboa, Monte da CaparicaCaparicaPortugal
  3. 3.Centro de Álgebra da Universidade de LisboaLisbonPortugal
  4. 4.Departamento de Matemática, Instituto de Ciências ExatasUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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